Sim(u)2lating A + living Cell - Covert Systems Biology Lab

Bioengineering
Sim(u) lating
2
a + living
Cell
In creating the first complete computer
model of an entire single-celled organism,
biologists are forging a powerful new kind
of tool for illuminating how life works
By Markus W. Covert
44 Scientific American, January 2014
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Illustration by André Kutscherauer
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Markus W. Covert is an assistant professor of
bioengineering at Stanford University, where he
directs a laboratory devoted to systems biology.
HE CRUCIAL INSIGHT CAME TO ME AS I LEISURELY RODE MY BIKE HOME FROM WORK.
It was Valentine’s Day, 2008. While I cruised along, my mind mulled over
a problem that had been preoccupying me and others in my field for
more than a decade. Was there some way to simulate life—including all
the marvelous, mysterious and maddeningly complex biochemistry that
makes it work—in software?
A working computer model of living cells, even if it were somewhat sketchy and not quite accurate, would be a fantastically useful tool. Research biologists could try out ideas for experiments
before committing time and money to actually do them in the
laboratory. Drug developers, for example, could accelerate their
search for new antibiotics by homing in on molecules whose inhibition would most disrupt a bacterium. Bioengineers like myself
could transplant and rewire the genes of virtual microorganisms
to design modified strains having special traits—the ability to fluoresce when infected by a certain virus, say, or perhaps the power
to extract hydrogen gas from petroleum—without the risks involved in altering real microbes. Eventually, if we can learn to
make models sophisticated enough to simulate human cells,
these tools could transform medical research by giving investigators a way to conduct studies that are currently impractical because many kinds of human cells cannot be cultured.
But all that seemed like a pipe dream without a practical
way to untangle the web of interlinked chemical reactions and
physical connections that make living cells tick. Many previous
attempts, by my lab at Stanford University as well as others,
had run into roadblocks; some had failed outright.
But as I pedaled slowly through the campus that winter evening, I thought about the work I had been doing recently to record images and video of single living cells. That’s when it hit
me—a way to make a realistic, functional simulator: choose one
of the simplest single-celled microbes out there, a bacterium
called Mycoplasma genitalium, and build a model of an individual germ. Limiting the simulation to just one cell would
simplify the problem enough that we could, in principle, include every bit of biology known to occur in that cell—the unwinding of every rung of its twisted DNA ladder, the transcription of every message in that DNA into an RNA copy, the
manufacture of every enzyme and other protein made from
those RNA instructions, and the interactions among every one
of those actors and many others, all building to cause the cell to
grow and eventually divide into two “daughters.” The simula-
IN BRIEF
Computer models that can account for the function of
every gene and molecule in a cell could revolutionize how
we study, understand and design biological systems.
A comprehensive simulation of a common infectious
bacterium was completed last year and, while still imperfect, is already generating new discoveries.
Scientists are now building models of more complex
organisms. Their long-term goal is to simulate human
cells and organs in comparable detail.
46 Scientific American, January 2014
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tion would generate, nearly from first principles, the entire drama of single-celled life.
Previous attempts had always tried to simulate a whole colony of cells because that is how almost all the data we have on
cell behavior were collected: from populations, not individuals.
Advances in both biotechnology and computing, however, had
started to make single-cell studies much easier to do. Now, I
realized, the tools were at hand to try a different approach.
Ideas whirred around in my head. The minute I reached
home, I started sketching out plans for a simulator. The next
morning, I began writing software code for just a
couple of the many, many distinct processes that
go on in a living microorganism. Within a week, I
had completed several prototype modules, each
one a software representation of a particular cellular process. The modules were producing output that looked fairly realistic.
I showed the work to a handful of other biologists. Most of them thought I was nuts. But I
felt I was on to something, and two exceptional
and daring graduate students, Jonathan R. Karr
and Jayodita C. Sanghvi, saw enough potential
in the approach that they agreed to work with
me on the project.
Completing this model would mean creating
dozens of such modules, combing through nearly 1,000 scientific articles for biochemical data,
and then using those values to constrain and
tweak thousands of parameters, such as how tightly enzymes
bind to their target molecules and how often DNA-reading proteins bump one another off the double helix. I suspected that,
even with the diligent help of collaborators and graduate students, the project would take years—but I also had a hunch
that, at the end, it would work. There was no way to know for
sure, except to try.
the human genome. They synthesized the essential genes of one
Mycoplasma species and showed they functioned in a cell.
To me and other young biologists in the late 1990s, this gang
was Led Zeppelin: iconoclastic, larger-than-life personalities
playing music we had never heard before. Clyde Hutchinson, one
of the biologists in Venter’s band, said that the ultimate test of
our understanding of simple cells would come when someone
modeled one in a computer. You can build a functional cell in the
lab by combining pieces without understanding every detail of
how they fit together. The same is not true of software.
I showed the sample
code to a handful
of other biologists.
Most of them thought
I was nuts. But I felt I
was on to something.
A GRAND CHALLENGE
As we set our sights on summiting this mountain, we took inspiration from the researchers who first dreamed of modeling life.
In 1984 Harold Morowitz, then at Yale University, laid out the
general route. He observed at the time that the simplest bacteria
that biologists had been able to culture, the mycoplasmas, were a
logical place to start. In addition to being very small and relatively simple, two species of Mycoplasma cause disease in humans:
the sexually transmitted, parasitic germ M. genitalium, which
thrives in the vaginal and urinary tracts, and M. pneumoniae,
which can cause walking pneumonia. A model of either species
could be quite medically useful, as well as a source of insight into
basic biology.
The first step, Morowitz proposed, should be to sequence
the genome of the selected microbe. J. Craig Venter and his colleagues at The Institute for Genome Research (TIGR) completed that task for M. genitalium in 1995; it has just 525 genes.
(Human cells, in contrast, have more than 20,000.)
I was a graduate student in San Diego when, four years later, the TIGR team concluded that only 400 or so of those genes
are essential to sustain life (as long as the microbes are grown
in a rich culture medium). Venter and his co-workers went on
to found Celera and race the federal government to sequence
Morowitz, too, had called for building a cell simulator based
on genome data from Mycoplasma. He argued that “every ex­­
periment that can be carried out in the lab can also be carried
out on the computer. The extent to which these [experimental
and simulation results] match measures the completeness of the
paradigm of molecular biology”—our working theory of how the
DNA and other biomolecules in the cell interact to yield life as
we know it. As we put the puzzle together, in other words, it be­­
comes more obvious which pieces and which interactions our
theory is missing.
Although high-throughput sequencers and robotic lab equipment have greatly accelerated the search for the missing pieces,
the floods of DNA sequences and gene activity patterns that
they generate do not come with explanations for how the parts
all fit together. The pioneering geneticist Sydney Brenner has
called such work “low-input, high-throughput, no-output” biology because too often the experiments are not driven by hy­­
potheses and yield disappointingly few insights about the larger systems that make life function—or malfunction.
This situation partly explains why, despite headlines regularly proclaiming the discovery of new genes associated with
cancer, obesity or diabetes, cures for these diseases remain frustratingly elusive. It appears that cures will come only when we
untangle the dozens or even hundreds of factors that interact,
sometimes in unintuitive ways, to cause these illnesses.
The pioneers of cell modeling understood that simulations of
whole cells that included all cellular components and their webs
of interactions would be powerful tools for making sense of such
jumbled, piecemeal data. By its nature, a whole-cell simulator
would distill a comprehensive set of hypotheses about what is
go­ing on inside a cell into rigorous, mathematical algorithms.
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The cartoonlike sketches one often sees in journal articles show­
ing that factor X regulates gene Y ... somehow ... are not nearly
precise enough for software. Programmers express these pro­
cesses as equations—one of the simpler examples is Y = aX + b—
even if they have to make educated guesses as to the values of
variables such as a and b. This demand for precision ultimately
reveals which laboratory experiments must be done to fill holes
in knowledge of reaction rates and oth­
er quantities.
At the same time, it was clear that
once models had been verified as accu­
rate, they would take the place of some
experiments, saving the costly “wet”
work for questions not answerable by
simulations alone. And simulated exper­
iments that generated surprising results
would help investigators to prioritize
their research and increase the pace of
scientific discovery. In fact, models of­­
fered such tempting tools for untangling
cause and effect that, in 2001, Masaru
Tomita of Keio University in Japan called
whole-cell simulation “a grand challenge
of the 21st century.”
When still a graduate student, I was
impressed by the early results of the leading cell modelers of
the time [see box on opposite page], and I became obsessed
with this grand challenge. Even as I set up my own lab and fo­­
cused on developing techniques for imaging single cells, the
challenge remained in my thoughts. And then, on that Febru­
ary bicycle ride home, I saw a way to meet it.
studies had done—could give us that constraint we needed.
Consider growth and reproduction. A large population of cells
grows incrementally; the birth or death of an individual cell
does not change things much. But for a single cell, division is a
very dramatic event. Before it splits in two, the organism has to
double its mass—and not just its overall mass. The amounts of
DNA, cell membrane and every kind of protein needed for sur­
As I flipped through the
plots and visualizations,
my heart began to
race. The model was
up and running. What
would it teach us?
TWO CRUCIAL INSIGHTS
It was clear that before we could simulate the life cycle of a mi­­
crobial species accurately enough to mimic its complex behav­
iors and make new discoveries in biology, we would have to
solve three problems. First, we needed to encode all the func­
tions that matter—from the flow of energy, nutrients and reac­
tion products through the cell (that is, its metabolism), to the
synthesis and decay of DNA, RNA and protein, to the activity of
myriad enzymes—into mathematical formulas and software
algorithms. Second, we had to come up with an overarching
framework to integrate all these functions. The final problem
was in many ways the hardest: to set upper and lower limits for
each of the 1,700-odd parameters in the model so that they took
on values that were biologically accurate—or at least in the
right ballpark.
I understood that no matter how exhaustively we scrutinized
the literature about M. genitalium and its close relations for
those parameters (Karr, Sanghvi and I eventually spent two
years culling data from some 900 papers), we would have to
make do in some cases by making educated guesses or by using
results from experiments on very different kinds of bacteria,
such as Escherichia coli, to obtain certain numbers, such as how
long RNA transcripts hang around in the cell, on average, before
enzymes rip them apart to recycle their pieces. Without a way to
constrain and check those guesses, we had no hope of success.
In that aha! moment in 2008, I had realized that modeling a
single cell—rather than a bunch of cells, as almost all previous
vival must each double. If the scope of the model is constrained
to a single cell, the computer can actually count and track every
molecule during the entire life cycle. It can check whether all
the numbers balance as one cell becomes two.
Moreover, a single cell reproduces at essentially a set pace.
M. genitalium, for example, typically divides every nine to 10
hours in a normal lab environment. It rarely takes fewer than
six hours or more than 15. The requirement that the cell must
duplicate all of its contents on this strict schedule would allow
us to choose plausible ranges for many variables that would
otherwise have been indeterminate, such as those that control
when replication of the DNA begins.
I put together a team of physicists, biologists, modelers and
even a former Google software engineer, and we discussed what
mathematical approaches to use. Michael Shuler, a biomedical
engineer at Cornell University who was a pioneer in cell simula­
tion, had built impressive models from ordinary differential
equations. Bernhard Palsson, under whom I studied in San Diego,
had developed a powerful technique, called flux-balance analy­
sis, that worked well for modeling metabolism. But others had
shown that random chance is an important element in gene
transcription, and cell division obviously involves a change in
the geometry of the cell membrane; those other methods would
not address these aspects. Even as a grad student, I had realized
that no one technique could model all the functions of a cell;
indeed, my dissertation had demonstrated a way to link two dis­
tinct mathematical approaches into a single simulator.
We decided, therefore, to create the whole-cell model as a
collection of 28 distinct modules, each of which uses the algo­
rithm that best suits the biological process and the degree of
knowledge we have about it [see box on page 50]. This strategy
led to a patchwork collection of mathematical procedures, how­
ever. We needed to sew them all together somehow into one
cohesive whole.
48 Scientific American, January 2014
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TIMELINE OF PROGRESS
Milestones in
Modeling Cells
The long path to the author’s first work­
ing model of a single cell of a simple
bacterium, Mycoplasma genitalium, was
informed by the theoretical, genetic
and modeling efforts of other re­­
searchers. Designing a computer mod­
el of a human cell is sure to be harder
still, given the far greater complexity of
mammalian cells. Human cells, for ex­­
ample, contain nearly 40 times as many
genes, and those genes are packed into
sets of chromosomes that are far more
intricate in their physical structure and
in the patterns of information they con­
tain. Some critical intermediate steps
that need to be ac­­complished are listed
at the bottom right.
1967
Francis Crick and Sydney Brenner
formulate and propose “Project K:
‘The Complete Solution of E. coli,’ ”
an effort to figure out the “design”
of this common gut bacterium,
includ­ing fine details of its genetics,
energy processing and reproduction.
1984
Harold Morowitz, then at Yale Uni­ver­
sity, outlines a plan to sequence and
then model a Mycoplasma bacterium.
1984
A team led by Michael Shuler of Cornell
University presents a computer model
that uses differential equations to
capture most of the major biological
processes involved in the growth
of a single cell of Escherichia coli.
The model was not able to include
gene-level activity, because the E. coli
genome had not yet been sequenced.
SCIENCE SOURCE
1989–1990
Bernhard Palsson of the University
of Michigan releases a comprehensive
model of the metabolism of the
human red blood cell that includes
the effects of pH variation and low
blood glucose.
1995
J. Craig Venter of TIGR and his
colleagues complete the genome
sequence of M. genitalium.
single-celled BacteriUM Mycoplasma genitalium ( purple bodies)
is about as simple as life gets. Yet modeling its life cycle was no easy task.
1999
Masaru Tomita and his teammates
at Keio University in Japan construct
E-Cell, a cell-modeling system
based on differential equations that
includes 127 genes, most of them
from M. genitalium.
2002
The Alliance for Cellular Signaling,
a large collaboration of about
50 researchers, launches an ambitious
10-year, $10-million effort to model
mouse B cells of the immune system
and heart muscle cells. The project
generates some exciting data sets
but encounters difficulties
manipulating B cells in culture.
2002
Palsson, George Church of Harvard
University and Covert, along with
several others, complete a genomescale model of the metabolism of
elico­bacter pylori, a bacterium that
H
infects humans and can cause stomach
ulcers and stomach cancer.
2004
Palsson and Covert, along with three
others, publish a computational model
of all 1,010 genes involved in regulating
the metabolism and DNA transcription
of E. coli and show that the model
accurately predicts the results of lab
experiments on real bacteria.
What’s Next
• Complete a whole-cell model for
a more typical, better-studied
bacterium, such as E. coli.
• Model a single-celled eukaryote,
such as the yeast Saccharomyces
cerevisiae. In a eukaryote, the DNA
is packaged inside a membranebound nucleus, not free-floating
as it is in a bacterium.
2012
Covert and his co-workers publish
a whole-cell model of M. genitalium
that, for the first time, simulates
all the genes and known bio­
chemical processes in a selfreproducing organism.
2013
Covert and his colleagues show
that the model accurately predicts
the activity of several enzymes.
• Build a model of an animal cell that
can be easily cultured, such as a
macrophage (a kind of immune cell)
from a mouse.
• Construct a first-draft model of
a human cell—again, probably
a macrophage.
• Model other kinds of human cells,
especially those that play the most
important roles in common diseases.
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I N S I D E A V I R T UA L C E L L
The Simulator at Work
The author’s computer model of the infectious bacterium Mycoplasma genitalium represents almost every aspect of the life, growth and
replication of this microbe. No single mathematical approach can
simulate every biological function in the cell, so these functions are
divided among 28 distinct modules (labeled in cell below), which are
involved in the processing of DNA (purple), RNA (light blue), proteins (dark blue), and energy, nutrients and waste (pink). For each
module, the researchers selected whichever mathematical method
worked best—several examples are highlighted below.
The program begins with all modules running in a random
sequence to simulate one second of real time. Many input values
are drawn from a large table of variables representing their initial
states, and some values are selected from ranges or probability
functions. Researchers can simulate different scenarios by altering
the starting configuration.
After the first time step, the program updates the state table
to reflect the outputs of all the modules. The sequence then runs
again for another one-second time step, updates the cell-state
table, and so on. The loop continues until the cell divides successfully, dies or becomes unrealistically old.
Metabolism of energy, nutrients and waste is modeled by using
flux-balance analysis, which exploits linear programming techniques
to calculate the reaction rates that produce optimal growth, energy
production or some other characteristic the modeler chooses. This
method assumes that the reactions occur rapidly enough to achieve
a steady state within the one-second time step of the simulation.
To prevent the first modules in the sequence from using up substances
needed by other modules, the simulator estimates each module’s fair
share of such resources and allocates them accordingly.
Decay and recycling of RNA and protein are modeled by using
Poisson processes, which make use of a random-number generator
and probability functions to decide whether a particular piece of RNA
or protein decays or survives to the next time step.
Protein
processing
Translation
of RNA into
proteins
RNA
decay
DNA
repair
Protein
activation
DNA
damage
Protein
modification
Protein
complex
formation
Transcription
regulation
DNA
supercoiling
Protein
folding
FtsZ polymer
formation
Chromosome Division of the
condensation cell contents
Chromosome
segregation
DNA
replication
Reactants and products of metabolism
DNA in the chromosomes
RNA copies of DNA segments
Enzymes and other proteins
External nutrients
Transcription
Replication
initiation
Host
interaction
Protein
decay
RNA
processing
Metabolism
Protein
sorting and
distribution
SOURCE: “A WHOLE-CELL COMPUTATIONAL MODEL PREDICTS PHENOTYPE FROM GENOTYPE,” BY JONATHAN R. KARR ET AL., IN CELL, VOL. 150, NO. 2; JULY 20, 2012
Input from the
environment
Assembly of the proteinmaking ribosomes
Transfer RNA
linking to
amino acids
RNA modification
Assembly of the
host-attachment
structure
Formation of the dividing ring is simulated by a hybrid model of two
parts. The ring, made of FtsZ polymers, grows into a wall that cleaves
the cell membrane in two during replication. In the first part of the
model, a set of differential equations estimates the growth of the FtsZ
ring by polymerization. In the second part, a geometric model of
filament bending simulates the ring, gradually pinching the ellipsoidal
cell near its midpoint until the organism splits into two daughter cells.
Gene transcription and translation—the steps that make many
of the proteins needed for cell growth and duplication—are simulated
by multipart algorithms that include Markov models (which track
over time the states of the enzymes that copy genes from DNA into
RNA), probabilistic binding of these enzymes to the DNA, and linear
programming to allocate energy and other resources.
DNA damage and repair are also modeled in this nondeterministic way.
SCIENTIFIC AMERICAN ONLINE
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See examples of the simulator’s output at ScientificAmerican.com/jan2014/cell-model
Illustration by AXS Biomedical Animation Studio
11/15/13 4:34 PM
SOURCE: “A Whole-Cell Computational Model Predicts Phenotype from Genotype,” by Jonathan R. Karr et al., in Cell, Vol. 150, No. 2; July 20, 2012
I thought back to an undergraduate course I had taken on
chemical plant design. For the final class project, we used a powerful simulator package called HYSYS to sketch out a large refinery.
HYSYS let us design each principal reaction to occur in a separate
vessel. Pipes then connected the output of one vessel to the inputs
of others. This framework connected many different kinds of
chemical operations into an orderly, predictable system.
It occurred to me that this approach, with some modification, might work for our cell simulator if I was willing to make
an important, simplifying assumption: that even though all
these biological processes occur simultaneously in a living cell,
their actions are effectively independent over periods of less
than a second. If that assumption was sound, we could divide
the life of the cell into one-second ticks of the clock and run
each of the 28 modules, in order, for one tick before updating
the pool of cell variables. The model would capture all the in­­
ter­­connectedness of biochemistry—the reliance of gene transcription and DNA synthesis on the energy and nucleotides
produced by metabolism, for example—but only on timescales
greater than one second.
We had no theoretical proof that this would work. It was a
leap of faith.
While constructing our virtual cell, we put in software sensors to measure what was going on inside. Every run of the simulator, covering the entire life cycle of a single cell, churned out
500 megabytes of data. The numerical output flowed into a
kind of instrument panel—a collection of dozens of charts and
visualizations that, when printed, completely filled a binder.
The results were frustrating at first. For months, as we de­­
bugged the code, refined the math, and added more and better
lab-derived constraints for the parameters, the cell refused to
divide or behaved erratically. For a while it produced huge
amounts of the amino acid alanine and very little else.
Then, one day, our cybernetic germ reached the end of its cell
cycle and divided successfully. Even more exciting, the doubling
time was around nine hours, just like that of living M. genitalium. Many other readings were still way off, but we felt then that
success was within reach.
Months later I was at a two-day conference in Bethesda, Md.,
when I was called to the hotel’s front desk between sessions.
“Dr. Covert? This package came for you.”
Back in my room, I peeled open the box and pulled out a
binder. As I spent the next hours flipping through hundreds of
pages of plots and complex visualizations, my heart began to
race. The great majority of the data looked just like one would
expect from an actual growing cell. And the remainder was in­­
triguing—unexpected but biologically plausible. That is when I
knew we had reached the summit of that mountain that loomed
so large years ago. The first computer model of an entire living
organism was up and running. What would it teach us?
A WINDOW INTO THE LIFE OF A CELL
After about a year of applying our new tool, we still see fascinating things every time we peer inside the workings of the virtual microorganism as it handles the millions of details in­­
volved in living and reproducing. We found, to our surprise,
that proteins knock one another off the DNA shockingly often—
about 30,000 times during every nine-hour life cycle. We also
discovered that the microbe’s remarkably stable doubling peri-
od is actually an emergent property that arises from the complex interplay between two distinct phases of replication, each
of which independently varies wildly in duration. And the second-by-second records of the cell’s behavior have allowed us to
explain why it is that the cell stops dividing immediately when
certain genes are disabled but reproduces another 10 times be­­
fore dying when other essential genes are turned off. Those ad­­
ditional rounds of division can happen whenever the cell stockpiles more copies of the protein made from the gene than it
needs in one lifetime—the extra is passed on to its descendants,
which perish only when the store at last runs out. These initial
results are exciting, but we may need years to understand ev­­
erything that these simulations are telling us about how these
microbes, and cells in general, function.
Our work with M. genitalium is only the first of many steps
on the way to modeling human cells or tissues at the level of
genes and molecules. The model that we have today is far from
perfect, and mycoplasmas are about as simple as self-sustaining life-forms get. We have made all our simulations, source
code, knowledge base, visualization code and experimental
data freely available online, and we and other investigators are
already working to improve the simulator and extend it to a
variety of organisms, such as E. coli and the yeast Saccharomyces cerevisiae, both of which are ubiquitous in academic and
industrial labs.
In these species, the regulation of genes is much more complex, and the location within the cell at which events occur
is far more important. When those issues have been addressed,
I anticipate that the next target will be a mouse or human cell:
most likely a cell, such as a macrophage (an attack cell in
the immune system), that can be readily cultured and em­­
ployed as a source of measurements to both tune and validate
the model.
I cannot guess how far we are today from such technology.
Compared with bacteria, human cells have many more compartments and exhibit far greater genetic control, much of
which remains mysterious. Moreover, as team players within
multicellular tissues, human cells interact more intimately
with other cell types than bacteria do.
On February 13, 2008, I would have said that we were at
least a decade away from the goal of modeling the simplest cell,
and I would not have even considered attempting to model
anything more complex. Now we can at least conceive of trying
to simulate a human cell—if only to see how the software fails,
which will illuminate the many things we still need to learn
about our own cells. Even that would be a pretty big step. M o r e to E x p l o r e
The Dawn of Virtual Cell Biology. Peter L. Freddolino and Saeed Tavazoie in Cell, Vol. 150, No. 2, pages 248–250; July 20, 2012.
A Whole-Cell Computational Model Predicts Phenotype from Genotype.
Jonathan R. Karr et al. in Cell, Vol. 150, No. 2, pages 389–401; July 20, 2012.
Bridging the Layers: Toward Integration of Signal Transduction, Regulation
and Metabolism into Mathematical Models. Emanuel Gonçalves et al. in
Molecular Biosystems, Vol. 9, No. 7, pages 1576–1583; July 2013.
From our Archives
Cybernetic Cells. W. Wayt Gibbs; August 2001.
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